Descartes' Secret Notebook (1)

"The sciences are now masked; the masks lifted, they appear in all their beauty. To someone who can see the entire chain of the sciences, it would seem no harder to discern them than to do so with the sequence of all the numbers. Strict limits are prescribed for all spirits, and these limits may not be trespassed. If some, by a flaw of spirit, are unable to follow the principles of invention, they may at least appreciate the real value of the sciences, and this should suffice to bring them true judgment on the evaluation of all things."

   — Réne Descartes, Preambles

Aczel, Amir D. Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe. New York: Broadway Books, 2005. xiv, 273 pp. (The above quote can be found on pp. 38-39.)

While I recommend reading this in hard copy, you have a number of online options at your fingertips. Begin with the Publisher description. You can also read a sample text.You can read the whole book online at scribd.com. And if you have a compelling need to download yourself a pirated copy, you can also download a compressed file from Megaupload.

I've written on this blog before on the burgeoning genre of popularized history of philosophy. Often the ideas themselves are shortchanged, but the biographical narratives are compelling and vividly portray the social contexts of the times. I have been especially rewarded by a complex of books whose narratives (unintentionally) bleed into one another; they could almost be grouped as volumes in a single series:

Rebecca Goldstein, Betraying Spinoza: The Renegade Jew Who Gave Us Modernity;

Matthew Stewart, The Courtier and the Heretic: Leibniz, Spinoza, and the Fate of God in the Modern World;

Steven Nadler, The Best of All Possible Worlds: A Story of Philosophers, God, and Evil;

Russell Shorto, Descartes’ Bones: A Skeletal History of the Conflict Between Faith and Reason.

Aczel's book fits in here, too, especially as it intersects the narratives of Nadler and Shorto. While Descartes' coded secret notebook is ostensibly the subject of this book, it is in actuality a biography of Descartes, with the decoding of the notebook the climax of the tale. There are, of course, other biographies of Descartes. Here is one review:

Serfati, Michel. "Descartes, the Pioneer of the Scientific Revolution" [review of Desmond Clarke, Descartes: A Biography, Cambridge University Press, 2006], Notices of the AMS, vol. 55, no. 1, January 2008, pp. 44-49.

I have not found any awe-inspiring reviews of Aczel, but here are a few:

Book Review – Descartes’s Secret Notebook, 22 April 2009

Star Topology, 13 Jan. 2011

Descartes' Secret Notebook, Steve Zipp, 20 Jan. 2009

One interesting feature of this book is the incorporation of recent discoveries and scholarship concerning Descartes.

Aczel begins with an account of his encounter with Descartes' cryptic manuscript: actually, the original is lost, and Aczel is really looking at the insatiably curious Leibniz' transcription of Descartes' manuscript. Aczel recounts also how he came by the idea of writing this book. Then he tells the story of Leibniz's encounter with Descartes' hidden work. Some quotes from variously titled texts are adduced, along with Descartes' pseudonym Polybius. The encrypted notebook itself consisted of 16 pages, with alchemical and astrological symbols, obscure figures, and puzzling number sequences. Following this teaser, the book traces the entire course of Descartes' life.

Descartes was the progeny of a wealthy family, endowed also with a tremendous curiosity, an ability to master a variety of skills and a wide range of knowledge, with an especial brilliance in mathematics. He was particularly fascinated by Greek mathematics, and by the power and limitations of what the Greeks could construct with straightedge and compass alone. Descartes was also quite the adventurer, joining in several military escapades, apparently motivated by curiosity rather than partisanship, even taking the side of Protestants in some campaigns though he himself was a lifelong Catholic. (Descartes was a confident swordsman who on one occasion fended off a boatload of criminals he had hired who schemed to assault him and steal his money [pp. 93-95]. He also got caught up in a duel over a woman [pp. 123-125].) Because of his extraordinary ability to solve mathematical problems, Descartes befriended a Dutchman whom he met as a soldier, Isaac Beeckman. They shared a considerable range of knowledge. (Note Descartes' letters to Beeckman of March 26 and April 29, 1619 on Ramon Llull, pp. 47-48.) This is where Descartes' curiosity about mystical ideas was aroused.

Chapter 4 recounts the key dreams that inspired Descartes, his notations in the text Olympica, and the possibility of a meeting with Kepler. Chapter 5 concerns the Athenians' obstacle in doubling the size of the Apollo Temple, a mathematical problem that cannot be solved by straightedge and compass alone. The Delian Problem, as it is known, stumped the Greeks. Descartes' meditation on this problem led him to the mathematical revolution he initiated: the unification of geometry and algebra.

Chapter 6 details the key meeting with the mystic-mathematician Johann Faulhaber of Ulm. We also find a confirmation that Descartes planned to write a mathematical treatise under the pseudonym Polybius the Cosmopolitan. In his notebook Descartes used alchemical symbols used by Faulhaber (pp. 74-75). Faulhaber was interested in the Kabbalah as well as in alchemy. Descartes' solved Faulhaber's mathematical problems. While engaged in a military campaign in Prague, Descartes noted in Olympica on 11 November 1620 a great discovery (p. 79).

In the following chapter we are introduced to the Brotherhood of the Rosy Cross, or the Rosicrucians, who were cosmopolitan philosophical revolutionaries. Descartes was heavily influenced by the Rosicrucians, so much so that he had to publicly deny any such allegiance, whether or not he was covertly a Rosicrucian. (This rumor also disturbed his close friend Mersenne, a Catholic priest albeit more progressive than most.) Descartes was quite interested in occult matters, and the Rosicrucians were also leaders in mathematical and scientific investigation. Faulhaber was a Rosicrucian. Kepler at least had a Rosicrucian assistant, if he was not one himself. Leibniz, who examined Descartes' notebook, was a Rosicrucian.

I am leaving out of account several details of Descartes' life: his bon vivant lifestyle as well as his periodic retreats into solitude—in hiding even—his military adventures, his interests in women, his financial affairs, etc. The most puzzling aspect of Descartes' character is his investment but apparent detachment regarding military affairs. Aczel finally addresses this question at the end of Chapter 11, after detailing Descartes' participation as a scientific observer in the brutal siege of La Rochelle, in which the population was starved out in the course of its military defeat. Descartes had no animosity against the Huguenots, who were crushed by the Catholic power, or against Protestants in general, whom he had fought for. Aczel attempts to explain Descartes by noting that he was trained by the Jesuits and was inducted into and attracted to military order and structure. In the 17th century, war was conducted in a highly and visibly ordered manner. (pp. 129-130)

This might be one of the more telling indications of the contradictions of the birth of modernity. If I believed in the notion of "instrumental reason" as a fundamental explanatory category, here I would find a key target, as I would in the other unresolved dualities of religion and reason, occultism and science, omnipotent mind/immortal soul and mechanical body.